Percolation-to-hopping crossover in conductor-insulator composites

Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few characteristics of the composite. Specifically, we find that the relevant parameters that give rise to one regime or the other are $D/\xi$ (where $D$ is the size of the conducting particles and $\xi$ is the tunneling length) and the specific composite microstructure. For large values of $D/\xi$, percolation arises when the composite microstructure can be modeled as a regular lattice that is fractionally occupied by conducting particle, while the tunneling regime is always obtained for equilibrium distributions of conducting particles in a continuum insulating matrix. As $D/\xi$ decreases the percolating behavior of the conductivity of lattice-like composites gradually crosses over to the tunneling-like regime characterizing particle dispersions in the continuum. For $D/\xi$ values lower than $D/\xi\simeq 5$ the conductivity has tunneling-like behavior independent of the specific microstructure of the composite.Comment: 8 pages, 5 figure

Dielectric response of a polar fluid trapped in a spherical nanocavity

We present extensive Molecular Dynamics simulation results for the structure, static and dynamical response of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii $R=2.5$, 3, and 4 nm embedded in a dielectric continuum of permittivity $\epsilon' \geq 1$. The polarisation of the external medium by the charge distribution inside the cavity is accounted for by appropriate image charges. We focus on the influence of the external permittivity $\epsilon'$ on the static and dynamic properties of the confined fluid. The density profile and local orientational order parameter of the dipoles turn out to be remarkably insensitive to $\epsilon'$. Permittivity profiles $\epsilon(r)$ inside the spherical cavity are calculated from a generalised Kirkwood formula. These profiles oscillate in phase with the density profiles and go to a ``bulk'' value $\epsilon_b$ away from the confining surface; $\epsilon_b$ is only weakly dependent on $\epsilon'$, except for $\epsilon' = 1$ (vacuum), and is strongly reduced compared to the permittivity of a uniform (bulk) fluid under comparable thermodynamic conditions. The dynamic relaxation of the total dipole moment of the sample is found to be strongly dependent on $\epsilon'$, and to exhibit oscillatory behaviour when $\epsilon'=1$; the relaxation is an order of magnitude faster than in the bulk. The complex frequency-dependent permittivity $\epsilon(\omega)$ is sensitive to $\epsilon'$ at low frequencies, and the zero frequency limit $\epsilon(\omega=0)$ is systematically lower than the ``bulk'' value $\epsilon_b$ of the static primitivity.Comment: 12 pages including 17 figure

Normal ground state of dense relativistic matter in a magnetic field

The properties of the ground state of relativistic matter in a magnetic field are examined within the framework of a Nambu-Jona-Lasinio model. The main emphasis of this study is the normal ground state, which is realized at sufficiently high temperatures and/or sufficiently large chemical potentials. In contrast to the vacuum state, which is characterized by the magnetic catalysis of chiral symmetry breaking, the normal state is accompanied by the dynamical generation of the chiral shift parameter $\Delta$. In the chiral limit, the value of $\Delta$ determines a relative shift of the longitudinal momenta (along the direction of the magnetic field) in the dispersion relations of opposite chirality fermions. We argue that the chirality remains a good approximate quantum number even for massive fermions in the vicinity of the Fermi surface and, therefore, the chiral shift is expected to play an important role in many types of cold dense relativistic matter, relevant for applications in compact stars. The qualitative implications of the revealed structure of the normal ground state on the physics of protoneutron stars are discussed. A noticeable feature of the $\Delta$ parameter is that it is insensitive to temperature when $T \ll \mu_0$, where $\mu_0$ is the chemical potential, and {\it increases} with temperature for $T > \mu_0$. The latter implies that the chiral shift parameter is also generated in the regime relevant for heavy ion collisions.Comment: 28 pages, 6 figures; v2: title changed in journa

Budding and vesiculation induced by conical membrane inclusions

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membrane-mediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.Comment: 11 pages, 12 figure

Time delay occultation data of the Helios spacecraft for probing the electron density distribution in the solar corona

S-band time delay measurements were collected from the spacecraft Helios A and B during three solar occultations in 1975/76 within heliocentric distances of about 3 and 215 earth radius in terms of range, Doppler frequency shift, and electron content. Characteristic features of measurement and data processing are described. Typical data sets are discussed to probe the electron density distribution near the sun (west and east limb as well) including the outer and extended corona. Steady-state and dynamical aspects of the solar corona are presented and compared with earth-bound-K-coronagraph measurements. Using a weighted least squares estimation, parameters of an average coronal electron density profile are derived in a preliminary analysis to yield electron densities at r = 3, 65, 215 earth radius. Transient phenomena are discussed and a velocity of propagation v is nearly equal to 900 km/s is determined for plasma ejecta from a solar flare observed during an extraordinary set of Helios B electron content measurements

Coarse-graining diblock copolymer solutions: a macromolecular version of the Widom-Rowlinson model

We propose a systematic coarse-grained representation of block copolymers, whereby each block is reduced to a single ``soft blob'' and effective intra- as well as intermolecular interactions act between centres of mass of the blocks. The coarse-graining approach is applied to simple athermal lattice models of symmetric AB diblock copolymers, in particular to a Widom-Rowlinson-like model where blocks of the same species behave as ideal polymers (i.e. freely interpenetrate), while blocks of opposite species are mutually avoiding walks. This incompatibility drives microphase separation for copolymer solutions in the semi-dilute regime. An appropriate, consistent inversion procedure is used to extract effective inter- and intramolecular potentials from Monte Carlo results for the pair distribution functions of the block centres of mass in the infinite dilution limit.Comment: To be published in mol.phys(2005

Surface melting of the vortex lattice

We discuss the effect of an (ab)-surface on the melting transition of the pancake-vortex lattice in a layered superconductor within a density functional theory approach. Both discontinuous and continuous surface melting are predicted for this system, although the latter scenario occupies the major part of the low-field phase diagram. The formation of a quasi-liquid layer below the bulk melting temperature inhibits the appearance of a superheated solid phase, yielding an asymmetric hysteretic behavior which has been seen in experiments.Comment: 4 pages, 3 figure

Failure properties of loaded fiber bundles having a lower cutoff in fiber threshold distribution

Presence of lower cutoff in fiber threshold distribution may affect the failure properties of a bundle of fibers subjected to external load. We investigate this possibility both in a equal load sharing (ELS) fiber bundle model and in local load sharing (LLS) one. We show analytically that in ELS model, the critical strength gets modified due to the presence of lower cutoff and it becomes bounded by an upper limit. Although the dynamic exponents for the susceptibility and relaxation time remain unchanged, the avalanche size distribution shows a permanent deviation from the mean-fiels power law. In the LLS model, we analytically estimate the upper limit of the lower cutoff above which the bundle fails at one instant. Also the system size variation of bundle's strength and the avalanche statistics show strong dependence on the lower cutoff level.Comment: 7 pages and 7 figure

Scattering and pair production by a potential barrier

Scattering and electron-positron pair production by a one-dimensional potential is considered in the framework of the $S-$matrix formalism. The solutions of the Dirac equation are classified according to frequency sign. The Bogoliubov transformation relating the in- and out-states are given. We show that the norm of a solution of the wave equation is determined by the largest amplitude of its asymptotic form when $x_3\to \pm\infty$. For a number of potentials we give the explicit expressions for the complete in- and out-sets of orthonormalized wave functions. We note that in principle virtual vacuum processes in external field influence the phase of wave function of scattered particle..Comment: 13 pages, LATEX 2e, no figure